PREPARED FOR THE U.S. DEPARTMENT OF ENERGY,UNDER CONTRACT DE-AC02-76CH03073

PRINCETON PLASMA PHYSICS LABORATORYPRINCETON UNIVERSITY, PRINCETON, NEW JERSEY

PPPL-3753 PPPL-3753UC-70

Physics Considerations in the Design of NCSX

by

G.H. Neilson, M.C. Zarnstorff, L.P. Ku, E.A. Lazarus, P.K. Mioduszewski,M. Fenstermacher, E. Fredrickson, G.Y. Fu, A. Grossman, P.J. Heitzenroeder,

R.H. Hatcher, S.P. Hirshman, S.R. Hudson, D.W. Johnson, H.W. Kugel,J.F. Lyon, R. Majeski, D.R. Mikkelsen, D.A. Monticello, B.E. Nelson,

N. Pomphrey, W.T. Reiersen, A.H. Reiman, P.H. Rutherford,J.A. Schmidt, D.A. Spong, and D.J. Strickler

October 2002

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1 IAEA-CN-94/IC-1

Physics Considerations in the Design of NCSX*

G. H. Neilson1, M. C. Zarnstorff1, L. P. Ku1, E. A. Lazarus2, P. K. Mioduszewski2,M. Fenstermacher3, E. Fredrickson1, G. Y. Fu1, A. Grossman4, P. J. Heitzenroeder1,R. H. Hatcher1, S. P. Hirshman2, S. R. Hudson1, D. W. Johnson1, H. W. Kugel1, J. F. Lyon2,R. Majeski1, D. R. Mikkelsen1, D. A. Monticello1, B. E. Nelson2, N. Pomphrey1,W. T. Reiersen1, A. H. Reiman1, P. H. Rutherford1, J. A. Schmidt1, D. A. Spong2,D. J. Strickler2

1) Princeton Plasma Physics Laboratory, Princeton, NJ 085432) Oak Ridge National Laboratory, Oak Ridge, TN 378313) Lawrence Livermore National Laboratory, Livermore, CA 94550.4) University of California at San Diego, San Diego, CA 92093

e-mail contact of main author: hneilson@pppl.gov

Abstract. Compact stellarators have the potential to make steady-state, disruption-free magnetic fusion systemswith β ~ 5% and relatively low aspect ratio (R/⟨a⟩ < 4.5) compared to most drift-optimized stellarators. Magneticquasi-symmetry can be used to reduce orbit losses. The National Compact Stellarator Experiment (NCSX) isdesigned to test compact stellarator physics in a high-beta quasi-axisymmetric configuration and to determine theconditions for high-beta disruption-free operation. It is designed around a reference plasma with low ripple, goodmagnetic surfaces, and stability to the important ideal instabilities at β ~ 4%. The device size, available heatingpower, and pulse lengths provide access to a high-beta target plasma state. The NCSX has magnetic flexibility toexplore a wide range of equilibrium conditions and has operational flexibility to achieve a wide range of betaand collisionality values. The design provides space to accommodate plasma-facing components for divertoroperation and ports for an extensive array of diagnostics.

1. Introduction

Fusion energy research is increasingly focused on the challenge of finding the best magneticconfiguration for a practical fusion reactor. Stellarators are of particular interest because theycan solve two major problems for magnetic confinement– achieving steady state operationand avoiding disruptions. Consequently, substantial investments are being made in newstellarator facilities, including the large superconducting LHD [1] and W7-X [2] experiments.The three-dimensional plasma geometry of stellarators provides degrees of freedom, notavailable in axisymmetric configurations, to target favorable physics properties (low magneticfield ripple, well-confined particle orbits, high-beta stability without the need for current driveor feedback) in their design. Design features now being studied experimentally include theuse of helical magnetic-axis excursions (TJ-II [3], H1-NF [4], and Heliotron-J [5]) andapproximate alignment of particle drift orbits with magnetic surfaces (W7-AS [6] andW7-X [2]).

In quasi-symmetric stellarator design the 3D magnetic field strength has an approximatesymmetry direction in Boozer coordinates [7] to keep charged particle drift orbits wellconfined. Compact stellarators are designed with an aspect ratio R/⟨a⟩ much less than that ofcurrentless optimized stellarators (≤ 4.5 vs. ≥ 10). Stellarator coils are designed to generatemost of the rotational transform and to shape the plasma to achieve the desired physics

* Research supported by the U.S. Department of Energy under Contract No. DE-AC76-CH0-

3073 with the Princeton Plasma Physics Laboratory and Contract No. DE-AC05-00OR-22725 with the Oak Ridge National Laboratory.

2 IAEA-CN-94/IC-1

properties. The bootstrap current can beused to generate some of the rotationaltransform (iota). Care must be taken in thedesign to minimize islands which are afeature of the three-dimensional geometry.

The National Compact Stellarator Experi-ment (NCSX) [8, 9] is designed to be aquasi-axisymmetric stellarator (QAS), sothat its transport properties are similar tothose of tokamaks. The design has highbeta (> 4%), moderate aspect ratio (≤ 4.4),and “reversed” magnetic shear. Asuccessful experimental test of magneticquasi-symmetry has already been carriedout in the Helically Symmetric Experiment(HSX) [10]. The mission of NCSX is to testcompact stellarator physics in a high-betaQAS configuration and to determine theconditions for high-beta disruption-freeoperation in order to evaluate its potential as a fusion concept. A QAS strategy is also used inthe CHS-qa study [11]. A quasi-poloidal, compact stellarator with lower aspect ratio is beingdesigned for the QPS experiment [12].

2. Coil Design

The NCSX uses modular coils (Fig. 1) to generate the main helical magnetic field. Forequilibrium flexibility, there are also toroidal field coils, poloidal field coils, and helical-fieldtrim coils. The physics basis for the coil design is a computed three-period reference QASplasma with β = 4%. An assumed moderately broad pressure profile typical of experimentsand a consistent bootstrap current profile which generates about one-fourth of the rotationaltransform at the edge areused.

Existing stellarator coildesign methods, based onthe VMEC [13] equil-ibr ium code, wereextended in order to designfeasible coils and plasmasfor low-aspect-ratio stellar-ators with internal currents.An initial filamentarymodular coil solution isfound by minimizing theroot-mean-squared normalcomponent of the magneticfield on the surface of thereference plasma, follow-ing the “reverse engineer-

FIG. 1. NCSX modular coils and referenceplasma.

FIG. 2. Poincaré plots of PIES magnetic surfaces for target free-boundary PIES equilibrium at β=4.1% for finite-cross sectionmodel of NCSX coils. Dashed line: first wall; solid line: VMECequilibrium boundary.

3 IAEA-CN-94/IC-1

ing” approach used in the W7-X design [14]. The coil geometry is then modified by atechnique which couples the coil [15] and plasma optimization processes to directly designcoils which produce a free-boundary target equilibrium possessing the reference plasmaphysics properties (rather than a particular shape), as well as engineering parameters such ascoil spacing and bend radius. The achieved physics properties are summarized in Table I. Aneffective ripple parameter εh, characterizing transport in the 1/ν regime [16], measures thedegree of quasi-axisym-metry. In the final step, thecoil geometry is modifiedagain using a technique toreduce the width of resid-ual islands in the free-boundary equilibriumcalculated by the PIEScode [17]. The coil designprocess leads to a free-boundary high-beta targetequilibrium that has goodmagnetic surfaces (Fig. 2)while preserving targetphysics and engineeringproperties.

Although optimized for asingle equilibrium, the

TABLE I. NCSX Configuration Physics Design Summary

Parameter orProperty

Achieved in ββββ = 4%Target Equilibrium Criteria

Aspect ratio R/⟨a⟩ 4.4Substantially lower than existing drift-optimized stellarator designs, e.g. HSX,W7-X.

Stability at⟨β⟩ = 4%

Stable to ext. kink,vertical, Mercier

modes

Sufficient to test stabilization of asustainable toroidal plasma by 3D shaping.

Sheariota = 0.39 (center),

0.65 (edge)

For neoclassical island reduction andhealing. Monotonically increasing exceptvery near the edge.

Large externaliota fraction.

~0.75 from coilsConservative approach for disruption-resistance.

Quasi-symmetryeffective ripple εh ≈

0.1% (center),0.4% (r/a ≈ 0.7).

Low helical ripple neoclassical transportcompared to axisymmetric designs;tolerable balanced neutral-beam-injectedion losses in high-beta, low-B scenarios.

Magnetic surfacequality

total effective islandwidth <10% of

toroidal flux

For negligible contribution to losses. Basedon PIES equilibrium calculations andestimated neoclassical and finite-χ⊥/χ||

island width corrections.

FIG. 3. Poincaré plots of PIES magnetic surfaces for vacuumconfiguration with iota of 0.43-0.46 (filamentary coil model).Dashed line: first wall; solid line: VMEC equilibrium boundary.

4 IAEA-CN-94/IC-1

NCSX coil design can support a broad range of equilibria with favorable physics propertiesand a wide range of plasma profiles, as is necessary for its mission. This is accomplished byvarying the currents in the toroidal field, poloidal field, and modular coil circuits. Since it isplanned to initiate NCSX plasmas on vacuum magnetic surfaces, the existence of goodvacuum configurations is critical. A vacuum case with iota < 0.5 everywhere, is shown inFig. 3. Good configurations with iota > 0.5 are also available, providing flexibility to eitherencounter or avoid possible instabilities associated with the iota = 0.5 resonance duringstartup.

The coil design provides a wide operating space in β and plasma current (IP) for the referencepressure and current profile shapes and constant magnetic field (B = 1.7 T at R = 1.4 m). Asshown in Fig. 4, VMEC equilibria stable to external kink and ballooning modes and havinglow ripple εh can be made with β ranging from 0 to 4% and IP from 0 to 100% of its referencevalue. Stable equilibria at higher beta (at least 6%) can be made with modest increase inripple. The design is robust to variations in pressure and current profile shapes. While thereference current profile is hollow, stable equilibria with β = 3%, and εh < 0.5% are foundwith peaked current profiles as well.

By varying coil currents, the equilibrium parameters to which the physics properties aresensitive can be varied, providing the capability to test theoretical predictions. Kink stabilitybeta limits can be lowered from the nominal 4% to about 1% so theoretical stability limits canbe studied over a range of beta values. While the design has been optimized to make theeffective ripple at r/a ≈ 0.7 very low, it can easily be increased by almost an order ofmagnitude, while preserving stability, to test the dependence of neoclassical losses andconfinement enhancement on the degree of quasi-symmetry. The rotational transform profilecan be varied to study its effects on transport and stability. The external rotational transformcan be varied at fixed shear from –0.2 to +0.1 about the reference profile. The global shear(ιedge - ι0) can be increased by a factor of 2 at fixed ι0; limits on reducing the shear are stillbeing studied.

Satisfactory magnetic surfaces have been calculated with PIES for several points in the NCSXoperating space, but additional island width control may be needed. Planned resonant trimcoils can be added to provide additional control of island-producing resonances for purposesof reducing island widths or performing controlled island physics experiments.

Beta (%)0 1 2 3 4 5 6

0 0.82% 0.89% 0.79%44 0.77% 0.68% 0.67% 0.61% 0.72%88 0.71% 0.65% 0.51% 0.72% 0.60%131 0.52% 0.46% 0.42% 0.41% 0.45%174 0.37% 0.39% 0.36% 0.40% 0.45% 0.92%C

urre

nt (

kA)

200 0.81%

FIG. 4. Operating diagram in plasma current-beta space for NCSX coils and reference profiles.Effective ripple (εh) at r/a≈0.7 are identified for equilibria found stable to external kink and ballooning

modes. Shaded equilibria are unstable. Unmarked regions were not analyzed.

5 IAEA-CN-94/IC-1

3. Device Size and Performance

The NCSX device size (major radius R = 1.4 m), magnetic field range (B = 1.2-2.0 Tesla),pulse length (0.3-1.2 s) and plasma heating power (initially 3 MW) are set to produce theplasma conditions and profiles needed to test critical physics issues over a range of beta andcollisionality values. The device will be initially equipped with two of the four existing1.5-MW, 50-keV, 0.3-s neutral beam injectors, formerly used on the PBX-M experiment.They are arranged for balanced tangential injection to be able to balance rotational transformperturbations due to beam-driven currents. Monte Carlo beam slowing down calculationspredict 24% hydrogen beam ion loss for balanced injection at B = 1.2 T. Plasmas withβ = 2.6% and collisionality ν* = 0.25 are predicted with the initial 3-MW beam system,assuming an enhancement factor of 2.9 times the ISS95 [18] stellarator confinement timescaling, or 0.9 times an equivalent ITER-97P L-mode tokamak scaling [19]. With the fullcomplement of hydrogen neutral beams (6 MW) and these same confinement enhancementassumptions, the reference beta value of 4% and collisionality ν* = 0.25 predicted. The ISS95enhancement factor required to reach 4% beta is reduced to 1.8 by allowing the density to riseto the Sudo limit [20], with an attendant increase in collisionality.

The NCSX magnet system is designed for pulsed operating scenarios with magnetic fields upto 2.0 T (for 0.2 s) for low-collisionality plasma studies and pulse lengths up to 1.2 s (atB = 1.2 T) for experiments with pulse lengths long compared to current equilibration times.The magnet design also provides operating scenarios with plasma current up to 350 kA(providing a factor of 2 range for internal rotational transform flexibility). The neutral beampulse length can be increased to 0.5 s with modest changes and potentially to >1 s withadditional upgrades. Radio frequency waves can be launched from the high-field side to moredirectly heat electrons than with the neutral beams.

4. Discharge Evolution

Time-dependent modeling of NCSX discharge evolution has been carried out to demonstratethe existence of satisfactory paths from vacuum fields to a target high-beta state, consistentwith the technical capabilities of the coils and heating systems. The coils are designed toprovide Ohmic heating, current drive, external rotational transform, and plasma shape control.Neutral beams provide plasma heating and current drive, although the balance of co- andcounter-injection is adjusted to minimize the latter. The bootstrap current provides significantrotational transform.

A simulation methodology based on the TRANSP 1-1/2-D tokamak analysis code wasdeveloped to model the time-evolution of the poloidal flux and iota profile. Because NCSX isquasi-axisymmetric, tokamak modeling tools can provide an accurate guide. An equivalenttokamak equilibrium is generated having the same external iota, major radius, aspect ratio,plasma volume, and toroidal flux as the reference NCSX equilibrium. In the simulation, theplasma shape, external iota profile (simulated as an externally-specified driven currentprofile), and density profile shape are kept constant in time. The plasma current, density,neutral beam heating power, and co-/counter- beam balance are programmed. The electronand ion thermal diffusivities are automatically adjusted to match an assumed global energyconfinement scaling (minimum of neo-Alcator and ITER-97P L-mode scaling). The TRANSPcode models poloidal flux diffusion, beam deposition and slowing down, neutral beam currentdrive, and power balance. It calculates the profiles of electron and ion temperature andpressure, fast ion pressure, current, and iota. The transformation to the actual NCSX geometry

6 IAEA-CN-94/IC-1

FIG. 6. Poincaré plots of PIES magnetic surfaces forequilibrium at t = 303 ms in discharge simulation. Dashedline: first wall; solid line: VMEC equilibrium boundary.

is accomplished by using the VMEC code to calculate a time-series of free-boundaryequilibria with the actual NCSX coil geometry and the TRANSP-simulated profiles as input.

Results are presented here for a simulation with B = 1.4 T and an available 6 MW of balancedneutral beam injection. Figure 5 shows time sequences of key input and output parameters ofthe 1-1/2-D modeling. Important aspects of discharge programming to obtain the target betaand a nearly stationary bootstrap current profile at the end of the discharge are minimizing theOhmic current during startup, adjusting the co-counter beam balance to approximatelybalance the Ohmic current profile, rapidly (~1.5 MA/s) increasing the current initiallyfollowed by clamping of the applied loop voltage, and modulating the neutral beam heatingpower to control the total pressure. At t = 303 ms of the TRANSP simulation, the averagetoroidal beta has risen to about 4% (corresponding to 4.5% when transformed to a stellaratorequilibrium because of a different magnetic field normalization), peak electron and iontemperatures are 2.4 keV and 2.8 keV respectively, and the volume-averaged electron andion collisionality values are νe* = 0.2, νi* = 0.1. The current (130 kA) is well matched to thebootstrap current (140 kA), and the current profile is predominantly bootstrap. The parametersand profiles in this state aresimilar , though notidentical, to those of thereference equilibrium. Free-boundary VMEC equilibriawere generated for thesequence of profilesresulting from this simu-lation and the NCSX coilsby varying the coil currentsto optimize physicsproperties. The plasma iscalculated to be stable toballooning, kink, andvertical modes and to havegood quasi-axisymmetry(εh < 0.4% at r/a ≈ 0.5)throughout the discharge.

0.1 0.2 0.3 0.4 0

100

(

kA )

Ip

IBS

0.1 0.2 0.3 0.4TIME (SECONDS)

0

1

2

3

4

5

βΤ

%

β

TIME (SECONDS)FIG. 5. Waveforms from time-dependent simulation of high-beta NCSX discharge.(a) Plasma current (programmed) and calculated bootstrap current. (b) Calculated betavalues using tokamak (βT) and stellarator (β) definitions.

7 IAEA-CN-94/IC-1

Magnetic surface quality is analyzed using the PIES code. Results at t = 303 ms, when 99% ofthe current is bootstrap, are shown in Fig. 6. The m = 5 island, which extends over 6.3% ofthe cross-section, is predicted to be reduced to 3% by neoclassical effects which are notincluded in the PIES calculations. The island widths can also be reduced using the trim coils.A number of small island chains are visible in Figure 5. When the island width is smallerthan a critical value, electron diffusion across the island dominates diffusion along the fieldline, and the presence of the island has little effect on transport. The critical island width isabout 2%-3% of the minor radius for the mode numbers of interest.

5. Power and Particle Handling

Control of impurities and neutral recycling is the main power and particle handling issue inthe design of NCSX. For impurity control, low-Z materials (carbon) are planned for surfaceswith intense plasma-wall interactions. For neutral control, recycling sources and baffles willbe arranged so as to inhibit neutral flow to the main plasma. Motivated in part by recentW7-AS divertor results showing improved edge control and plasma performance [21], theNCSX is designed so that a pumped slot divertor can be installed in the future. The basicrequirement affecting the design of the coils and the vacuum vessel is providing sufficientconnection length of field lines in the scrapeoff layer outside the last closed magneticsurface (LCMS). Connection lengths longer than 100 m are sufficient to allow hightemperatures at the LCMS andsignificant temperature drops alongfield lines to reasonably low targettemperatures, and hence theestablishment of low temperatures anda high recycling regime to control theimpurity source at the target.

Scrapeoff layer field-line followingcalculations f o r m a g n e t i cconfigurations which have finiteplasma pressure were made using theMFBE code [22]. In NCSX the fieldlines launched close to the LCMS(here taken to be the VMECboundary) make many toroidalrevolutions close to it and do notexhibit very strong stochasticity. Thisis seen in Fig. 7, a Poincaré plot ofscrapeoff field lines for the referencehigh-beta state and the NCSX coils.The field lines are launched from themidplane, half from the inside andhalf from the outside, from 0 to10 mm outside the LCMS. Most linesremain within a 4-cm wide bandconformal to the boundary (exceptnear the tips of the banana-shapedcross sections, where the divertorwould be located) long enough to

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1 1.2 1.4 1.6 1.8

Z (

m)

R (m)FIG. 7 Poincaré plots of scrapeoff field lines started atthe inboard and outboard midplane within 0-1 cm ofthe nominal (VMEC) boundary and followed for 20toroidal revolutions.

8 IAEA-CN-94/IC-1

complete 20 toroidal revolutions (~200 m) and provide the required connection lengths. Thesecalculations are used as a guide in the placement of plasma-facing components with sufficientclearance to provide long connection lengths.

6. Summary

The NCSX is designed to provide the capabilities needed to assess the physics of compactstellarators. It will produce high beta equilibria with good physics properties and magneticsurfaces, have an ample operating space and flexibility, and provide access to high-beta targetequilibria starting from vacuum. Based on these physics considerations, a feasible engineeringconcept for the NCSX has been developed. [23] It provides the space and access provisions toaugment the initial configuration with new capabilities, particularly diagnostics [24] andplasma-facing components, as needed in the course of the experimental program. [1] FUJIWARA, M., et al., in Fusion Energy 2000 (Proc. 18th Conf., Sorrento, Italy, 4-10

Oct., 2000), IAEA, Vienna (2001), Paper IAEA-CN-77-OV1/4.[2] LOTZ, W., et al., in Plasma Physics and Controlled Nuclear Fusion Research 1990 (Proc.

13th Int. Conf. Washington, 1990) Vol.2, IAEA, Vienna (1991) 603.[3] ALEJALDRE, C., et al., in Fusion Energy 2000 (Proc. 18th Conf., Sorrento, Italy, 4-10

Oct., 2000), IAEA, Vienna (2001), Paper IAEA-CN-77-OV4/4.[4] HARRIS, J. H., et al., in Fusion Energy 2000 (Proc. 18th Conf., Sorrento, Italy, 4-10

Oct., 2000), IAEA, Vienna (2001), Paper IAEA-CN-77-EXP1/02.[5] OBIKI, T., et al., in Fusion Energy 2000 (Proc. 18th Conf., Sorrento, Italy, 4-10 Oct.,

2000), IAEA, Vienna (2001), Paper IAEA-CN-77-EXP1/09.[6] SAPPER, J. et al., Fusion Technol. 17 (1990) 62.[7] BOOZER, A. H., Phys. Fluids 23 (1980) 904.[8] ZARNSTORRF, M., et al., in Fusion Energy 2000 (Proc. 18th Conf., Sorrento, Italy,

4-10 Oct., 2000), IAEA, Vienna (2001), Paper IAEA-CN-77-IC/1.[9] NEILSON, G. H., et al., Phys. Plasmas 7 (2000) 1911.[10] TALMADGE, J. N., this conference, Paper IAEA-CN-94-EX/P3-22.[11] OKAMURA, S., et al., in Fusion Energy 2000 (Proc. 18th Conf., Sorrento, Italy, 4-10

Oct., 2000), IAEA, Vienna (2001), Paper IAEA-CN-77-ICP/16.[12] SPONG, D. A., et al., Nucl. Fusion 41 (2001) 711; LYON, J. F., et al., this conference,

Paper IAEA-CN-94-IC/P-05.[13] HIRSHMAN, S. P., et al. , Comput. Phys. Commun. 43 (1986) 143.[14] NÜHRENBERG, J. and ZILLE, R., Phys. Lett. A 129 (1988) 113.[15] STRICKLER D. J., BERRY L. A., and HIRSHMAN S. P., Fusion Sci. and Technol. 41

(2002) 107.[16] NEMOV, V V., et al., Phys. Plasmas 6 (1999) 4622.[17] HUDSON, S. R., et al., “Eliminating Islands in High-Pressure Free-Boundary Stellarator

Magnetohydrodynamic Equilibrium Solutions,” submitted to Phys. Rev. Lett.[18] STROTH, U., et al., Nuclear Fusion 36 (1996) 1063.[19] KAYE, S., et al., Nuclear Fusion 39 (1999) 1245.[20] SUDO, S., et al., Nuclear Fusion 30 (1990) 11.[21] GRIGULL, P. et al., 28th EPS Conference, Madeira, Portugal, 18-22 June, 2001[22] STRUMBERGER, E. et al., Nucl Fusion, 37 (1997) 19.[23] NELSON, B. E., et al., this conference, Paper IAEA-CN-94-FT/2-4.[24] JOHNSON, D., et al., “Diagnostics Plan for the National Compact Stellarator

Experiment,” Rev. Sci. Inst., to be published.

03/26/01

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